A Survey of Statistical Models for Reverse Engineering Gene Regulatory Networks

Disruption of lineage integrity as a precursor to breast tumor initiation

Increase in lineage infidelity and/or imbalance is frequently observed around the earliest stage of breast tumor initiation. In response to disruption of homeostasis, differentiated cells can partially lose their identity and gain cellular plasticity, a process involving epigenome landscape remodeling. This increase of cellular plasticity may promote the malignant transformation of breast tumors and fuel their heterogeneity. Here, we review recent studies that have yield insights into important regulators of lineage integrity and mechanisms that trigger mammary epithelial lineage derail, and evaluate their impacts on breast tumor development.

Deep Learning Enhances Multiparametric Dynamic Volumetric Photoacoustic Computed Tomography In Vivo (DL-PACT)

Photoacoustic computed tomography (PACT) has become a premier preclinical and clinical imaging modality. Although PACT's image quality can be dramatically improved with a large number of ultrasound (US) transducer elements and associated multiplexed data acquisition systems, the associated high system cost and/or slow temporal resolution are significant problems. Here, a deep learning-based approach is demonstrated that qualitatively and quantitively diminishes the limited-view artifacts that reduce image quality and improves the slow temporal resolution. This deep learning-enhanced multiparametric dynamic volumetric PACT approach, called DL-PACT, requires only a clustered subset of many US transducer elements on the conventional multiparametric PACT. Using DL-PACT, high-quality static structural and dynamic contrast-enhanced whole-body images as well as dynamic functional brain images of live animals and humans are successfully acquired, all in a relatively fast and cost-effective manner. It is believed that the strategy can significantly advance the use of PACT technology for preclinical and clinical applications such as neurology, cardiology, pharmacology, endocrinology, and oncology.

A Bi-Objective RNN Model to Reconstruct Gene Regulatory Network: A Modified Multi-Objective Simulated Annealing Approach

Gene Regulatory Network (GRN) is a virtual network in a cellular context of an organism, comprising a set of genes and their internal relationships to regulate protein production rate (gene expression level) of each other through coded proteins. Computational Reconstruction of GRN from gene expression data is a widely-applied research area. Recurrent Neural Network (RNN) is a useful modeling scheme for GRN reconstruction. In this research, the RNN formulation of GRN reconstruction having single objective function has been modified to incorporate a new objective function. An existing multi-objective meta-heuristic algorithm, called Archived Multi Objective Simulated Annealing (AMOSA), has been modified and applied to this bi-objective RNN formulation. Executing the resulting algorithm (called AMOSA-GRN) on a gene expression dataset, a collection (termed as Archive) of non-dominated GRNs has been obtained. Ensemble averaging has been applied on the archives, and obtained through a sequence of executions of AMOSA-GRN. Accuracy of GRNs in the averaged archive, with respect to gold standard GRN, varies in the range 0.875 - 1.0 (87.5 - 100 percent).

Gene Regulatory Networks Reconstruction Using the Flooding-Pruning Hill-Climbing Algorithm

The explosion of genomic data provides new opportunities to improve the task of gene regulatory network reconstruction. Because of its inherent probability character, the Bayesian network is one of the most promising methods. However, excessive computation time and the requirements of a large number of biological samples reduce its effectiveness and application to gene regulatory network reconstruction. In this paper, Flooding-Pruning Hill-Climbing algorithm (FPHC) is proposed as a novel hybrid method based on Bayesian networks for gene regulatory networks reconstruction. On the basis of our previous work, we propose the concept of DPI Level based on data processing inequality (DPI) to better identify neighbors of each gene on the lack of enough biological samples. Then, we use the search-and-score approach to learn the final network structure in the restricted search space. We first analyze and validate the effectiveness of FPHC in theory. Then, extensive comparison experiments are carried out on known Bayesian networks and biological networks from the DREAM (Dialogue on Reverse Engineering Assessment and Methods) challenge. The results show that the FPHC algorithm, under recommended parameters, outperforms, on average, the original hill climbing and Max-Min Hill-Climbing (MMHC) methods with respect to the network structure and running time. In addition, our results show that FPHC is more suitable for gene regulatory network reconstruction with limited data.

Computational Approaches to Study Gene Regulatory Networks

The goal of the gene regulatory network (GRN) inference is to determine the interactions between genes given heterogeneous data capturing spatiotemporal gene expression. Since transcription underlines all cellular processes, the inference of GRN is the first step in deciphering the determinants of the dynamics of biological systems. Here, we first describe the generic steps of the inference approaches that rely on similarity measures and group the similarity measures based on the computational methodology used. For each group of similarity measures, we not only review the existing approaches but also describe specifically the detailed steps of the existing state-of-the-art algorithms.

Variable neighborhood search for reverse engineering of gene regulatory networks

A new search heuristic, Divided Neighborhood Exploration Search, designed to be used with inference algorithms such as Bayesian networks to improve on the reverse engineering of gene regulatory networks is presented. The approach systematically moves through the search space to find topologies representative of gene regulatory networks that are more likely to explain microarray data. In empirical testing it is demonstrated that the novel method is superior to the widely employed greedy search techniques in both the quality of the inferred networks and computational time.

Time-Dependent Gene Network Modelling by Sequential Monte Carlo

Most existing methods used for gene regulatory network modeling are dedicated to inference of steady state networks, which are prevalent over all time instants. However, gene interactions evolve over time. Information about the gene interactions in different stages of the life cycle of a cell or an organism is of high importance for biology. In the statistical graphical models literature, one can find a number of methods for studying steady-state network structures while the study of time varying networks is rather recent. A sequential Monte Carlo method, namely particle filtering (PF), provides a powerful tool for dynamic time series analysis. In this work, the PF technique is proposed for dynamic network inference and its potentials in time varying gene expression data tracking are demonstrated. The data used for validation are synthetic time series data available from the DREAM4 challenge, generated from known network topologies and obtained from transcriptional regulatory networks of S. cerevisiae. We model the gene interactions over the course of time with multivariate linear regressions where the parameters of the regressive process are changing over time.

Data-based Reconstruction of Gene Regulatory Networks of Fungal Pathogens

In the emerging field of systems biology of fungal infection, one of the central roles belongs to the modeling of gene regulatory networks (GRNs). Utilizing omics-data, GRNs can be predicted by mathematical modeling. Here, we review current advances of data-based reconstruction of both small-scale and large-scale GRNs for human pathogenic fungi. The advantage of large-scale genome-wide modeling is the possibility to predict central (hub) genes and thereby indicate potential biomarkers and drug targets. In contrast, small-scale GRN models provide hypotheses on the mode of gene regulatory interactions, which have to be validated experimentally. Due to the lack of sufficient quantity and quality of both experimental data and prior knowledge about regulator–target gene relations, the genome-wide modeling still remains problematic for fungal pathogens. While a first genome-wide GRN model has already been published for Candida albicans, the feasibility of such modeling for Aspergillus fumigatus is evaluated in the present article. Based on this evaluation, opinions are drawn on future directions of GRN modeling of fungal pathogens. The crucial point of genome-wide GRN modeling is the experimental evidence, both used for inferring the networks (omics ‘first-hand’ data as well as literature data used as prior knowledge) and for validation and evaluation of the inferred network models.

A Maximum A Posteriori Probability and Time-Varying Approach for Inferring Gene Regulatory Networks from Time Course Gene Microarray Data

Unlike most conventional techniques with static model assumption, this paper aims to estimate the time-varying model parameters and identify significant genes involved at different timepoints from time course gene microarray data. We first formulate the parameter identification problem as a new maximum a posteriori probability estimation problem so that prior information can be incorporated as regularization terms to reduce the large estimation variance of the high dimensional estimation problem. Under this framework, sparsity and temporal consistency of the model parameters are imposed using L1-regularization and novel continuity constraints, respectively. The resulting problem is solved using the L-BFGS method with the initial guess obtained from the partial least squares method. A novel forward validation measure is also proposed for the selection of regularization parameters, based on both forward and current prediction errors. The proposed method is evaluated using a synthetic benchmark testing data and a publicly available yeast Saccharomyces cerevisiae cell cycle microarray data. For the latter particularly, a number of significant genes identified at different timepoints are found to be biological significant according to previous findings in biological experiments. These suggest that the proposed approach may serve as a valuable tool for inferring time-varying gene regulatory networks in biological studies.

Refining network reconstruction based on functional reliability

Reliable functioning is crucial for the survival and development of the genetic regulatory networks in living cells and organisms. This functional reliability is an important feature of the networks and reflects the structural features that have been embedded in the regulatory networks by evolution. In this paper, we integrate this reliability into network reconstruction. We introduce the concept of dependency probability to measure the dependency of functional reliability on network edges. We also propose a method to estimate the dependency probability and select edges with high contributions to functional reliability. We use two real examples, the regulatory network of the cell cycle of the budding yeast and that of the fission yeast, to demonstrate that the proposed method improves network reconstruction. In addition, the dependency probability is robust in calculation and can be easily implemented in practice.

Gene regulatory network inference by point-based Gaussian approximation filters incorporating the prior information

The extended Kalman filter (EKF) has been applied to inferring gene regulatory networks. However, it is well known that the EKF becomes less accurate when the system exhibits high nonlinearity. In addition, certain prior information about the gene regulatory network exists in practice, and no systematic approach has been developed to incorporate such prior information into the Kalman-type filter for inferring the structure of the gene regulatory network. In this paper, an inference framework based on point-based Gaussian approximation filters that can exploit the prior information is developed to solve the gene regulatory network inference problem. Different point-based Gaussian approximation filters, including the unscented Kalman filter (UKF), the third-degree cubature Kalman filter (CKF₃), and the fifth-degree cubature Kalman filter (CKF₅) are employed. Several types of network prior information, including the existing network structure information, sparsity assumption, and the range constraint of parameters, are considered, and the corresponding filters incorporating the prior information are developed. Experiments on a synthetic network of eight genes and the yeast protein synthesis network of five genes are carried out to demonstrate the performance of the proposed framework. The results show that the proposed methods provide more accurate inference results than existing methods, such as the EKF and the traditional UKF.

Construction and analysis of single nucleotide polymorphism-single nucleotide polymorphism interaction networks

The study of gene regulatory network and protein-protein interaction network is believed to be fundamental to the understanding of molecular processes and functions in systems biology. In this study, the authors are interested in single nucleotide polymorphism (SNP) level and construct SNP-SNP interaction network to understand genetic characters and pathogenetic mechanisms of complex diseases. The authors employ existing methods to mine, model and evaluate a SNP sub-network from SNP-SNP interactions. In the study, the authors employ the two SNP datasets: Parkinson disease and coronary artery disease to demonstrate the procedure of construction and analysis of SNP-SNP interaction networks. Experimental results are reported to demonstrate the procedure of construction and analysis of such SNP-SNP interaction networks can recover some existing biological results and related disease genes.

Reverse engineering sparse gene regulatory networks using cubature kalman filter and compressed sensing

This paper proposes a novel algorithm for inferring gene regulatory networks which makes use of cubature Kalman filter (CKF) and Kalman filter (KF) techniques in conjunction with compressed sensing methods. The gene network is described using a state-space model. A nonlinear model for the evolution of gene expression is considered, while the gene expression data is assumed to follow a linear Gaussian model. The hidden states are estimated using CKF. The system parameters are modeled as a Gauss-Markov process and are estimated using compressed sensing-based KF. These parameters provide insight into the regulatory relations among the genes. The Cramér-Rao lower bound of the parameter estimates is calculated for the system model and used as a benchmark to assess the estimation accuracy. The proposed algorithm is evaluated rigorously using synthetic data in different scenarios which include different number of genes and varying number of sample points. In addition, the algorithm is tested on the DREAM4 in silico data sets as well as the in vivo data sets from IRMA network. The proposed algorithm shows superior performance in terms of accuracy, robustness, and scalability.

Gene regulation, modulation, and their applications in gene expression data analysis

Common microarray and next-generation sequencing data analysis concentrate on tumor subtype classification, marker detection, and transcriptional regulation discovery during biological processes by exploring the correlated gene expression patterns and their shared functions. Genetic regulatory network (GRN) based approaches have been employed in many large studies in order to scrutinize for dysregulation and potential treatment controls. In addition to gene regulation and network construction, the concept of the network modulator that has significant systemic impact has been proposed, and detection algorithms have been developed in past years. Here we provide a unified mathematic description of these methods, followed with a brief survey of these modulator identification algorithms. As an early attempt to extend the concept to new RNA regulation mechanism, competitive endogenous RNA (ceRNA), into a modulator framework, we provide two applications to illustrate the network construction, modulation effect, and the preliminary finding from these networks. Those methods we surveyed and developed are used to dissect the regulated network under different modulators. Not limit to these, the concept of “modulation” can adapt to various biological mechanisms to discover the novel gene regulation mechanisms.

An overview of the statistical methods used for inferring gene regulatory networks and protein-protein interaction networks

The large influx of data from high-throughput genomic and proteomic technologies has encouraged the researchers to seek approaches for understanding the structure of gene regulatory networks and proteomic networks. This work reviews some of the most important statistical methods used for modeling of gene regulatory networks (GRNs) and protein-protein interaction (PPI) networks. The paper focuses on the recent advances in the statistical graphical modeling techniques, state-space representation models, and information theoretic methods that were proposed for inferring the topology of GRNs. It appears that the problem of inferring the structure of PPI networks is quite different from that of GRNs. Clustering and probabilistic graphical modeling techniques are of prime importance in the statistical inference of PPI networks, and some of the recent approaches using these techniques are also reviewed in this paper. Performance evaluation criteria for the approaches used for modeling GRNs and PPI networks are also discussed.

Comparative Genomics and Systems Biology of Malaria Parasites Plasmodium

Malaria is a serious infectious disease that causes over one million deaths yearly. It is caused by a group of protozoan parasites in the genus Plasmodium. No effective vaccine is currently available and the elevated levels of resistance to drugs in use underscore the pressing need for novel antimalarial targets. In this review, we survey omics centered developments in Plasmodium biology, which have set the stage for a quantum leap in our understanding of the fundamental processes of the parasite life cycle and mechanisms of drug resistance and immune evasion.

Developmental evolution in social insects: regulatory networks from genes to societies

The evolution and development of complex phenotypes in social insect colonies, such as queen-worker dimorphism or division of labor, can, in our opinion, only be fully understood within an expanded mechanistic framework of Developmental Evolution. Conversely, social insects offer a fertile research area in which fundamental questions of Developmental Evolution can be addressed empirically. We review the concept of gene regulatory networks (GRNs) that aims to fully describe the battery of interacting genomic modules that are differentially expressed during the development of individual organisms. We discuss how distinct types of network models have been used to study different levels of biological organization in social insects, from GRNs to social networks. We propose that these hierarchical networks spanning different organizational levels from genes to societies should be integrated and incorporated into full GRN models to elucidate the evolutionary and developmental mechanisms underlying social insect phenotypes. Finally, we discuss prospects and approaches to achieve such an integration.

Inferring gene regulatory networks via nonlinear state-space models and exploiting sparsity

This paper considers the problem of learning the structure of gene regulatory networks from gene expression time series data. A more realistic scenario when the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter-based state estimation algorithm is considered instead of the contemporary linear approximation-based approaches. The parameters characterizing the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then subjected to a LASSO-based least squares regression operation which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with the extended Kalman filter (EKF) and Unscented Kalman Filter (UKF) employing the Mean Square Error (MSE) as the fidelity criterion in recovering the parameters of gene regulatory networks from synthetic data and real biological data. Extensive computer simulations illustrate that the proposed particle filter-based network inference algorithm outperforms EKF and UKF, and therefore, it can serve as a natural framework for modeling gene regulatory networks with nonlinear and sparse structure.

Inference of gene regulatory subnetworks from time course gene expression data

Background

Identifying gene regulatory network (GRN) from time course gene expression data has attracted more and more attentions. Due to the computational complexity, most approaches for GRN reconstruction are limited on a small number of genes and low connectivity of the underlying networks. These approaches can only identify a single network for a given set of genes. However, for a large-scale gene network, there might exist multiple potential sub-networks, in which genes are only functionally related to others in the sub-networks.

Results

We propose the network and community identification (NCI) method for identifying multiple subnetworks from gene expression data by incorporating community structure information into GRN inference. The proposed algorithm iteratively solves two optimization problems, and can promisingly be applied to large-scale GRNs. Furthermore, we present the efficient Block PCA method for searching communities in GRNs.

Conclusions

The NCI method is effective in identifying multiple subnetworks in a large-scale GRN. With the splitting algorithm, the Block PCA method shows a promosing attempt for exploring communities in a large-scale GRN.

Stability of building gene regulatory networks with sparse autoregressive models

Background

Biological networks are constantly subjected to random perturbations, and efficient feedback and compensatory mechanisms exist to maintain their stability. There is an increased interest in building gene regulatory networks (GRNs) from temporal gene expression data because of their numerous applications in life sciences. However, because of the limited number of time points at which gene expressions can be gathered in practice, computational techniques of building GRN often lead to inaccuracies and instabilities. This paper investigates the stability of sparse auto-regressive models of building GRN from gene expression data.

Results

Criteria for evaluating the stability of estimating GRN structure are proposed. Thereby, stability of multivariate vector autoregressive (MVAR) methods - ridge, lasso, and elastic-net - of building GRN were studied by simulating temporal gene expression datasets on scale-free topologies as well as on real data gathered over Hela cell-cycle. Effects of the number of time points on the stability of constructing GRN are investigated. When the number of time points are relatively low compared to the size of network, both accuracy and stability are adversely affected. At least, the number of time points equal to the number of genes in the network are needed to achieve decent accuracy and stability of the networks. Our results on synthetic data indicate that the stability of lasso and elastic-net MVAR methods are comparable, and their accuracies are much higher than the ridge MVAR. As the size of the network grows, the number of time points required to achieve acceptable accuracy and stability are much less relative to the number of genes in the network. The effects of false negatives are easier to improve by increasing the number time points than those due to false positives. Application to HeLa cell-cycle gene expression dataset shows that biologically stable GRN can be obtained by introducing perturbations to the data.

Conclusions

Accuracy and stability of building GRN are crucial for investigation of gene regulations. Sparse MVAR techniques such as lasso and elastic-net provide accurate and stable methods for building even GRN of small size. The effect of false negatives is corrected much easier with the increased number of time points than those due to false positives. With real data, we demonstrate how stable networks can be derived by introducing random perturbation to data.

Biomolecular self-defense and futility of high-specificity therapeutic targeting

Robustness has been long recognized to be a distinctive property of living entities. While a reasonably wide consensus has been achieved regarding the conceptual meaning of robustness, the biomolecular mechanisms underlying this systemic property are still open to many unresolved questions. The goal of this paper is to provide an overview of existing approaches to characterization of robustness in mathematically sound terms. The concept of robustness is discussed in various contexts including network vulnerability, nonlinear dynamic stability, and self-organization. The second goal is to discuss the implications of biological robustness for individual-target therapeutics and possible strategies for outsmarting drug resistance arising from it. Special attention is paid to the concept of swarm intelligence, a well studied mechanism of self-organization in natural, societal and artificial systems. It is hypothesized that swarm intelligence is the key to understanding the emergent property of chemoresistance.

Bayesian non-negative factor analysis for reconstructing transcription factor mediated regulatory networks

Background

Transcriptional regulation by transcription factor (TF) controls the time and abundance of mRNA transcription. Due to the limitation of current proteomics technologies, large scale measurements of protein level activities of TFs is usually infeasible, making computational reconstruction of transcriptional regulatory network a difficult task.

Results

We proposed here a novel Bayesian non-negative factor model for TF mediated regulatory networks. Particularly, the non-negative TF activities and sample clustering effect are modeled as the factors from a Dirichlet process mixture of rectified Gaussian distributions, and the sparse regulatory coefficients are modeled as the loadings from a sparse distribution that constrains its sparsity using knowledge from database; meantime, a Gibbs sampling solution was developed to infer the underlying network structure and the unknown TF activities simultaneously. The developed approach has been applied to simulated system and breast cancer gene expression data. Result shows that, the proposed method was able to systematically uncover TF mediated transcriptional regulatory network structure, the regulatory coefficients, the TF protein level activities and the sample clustering effect. The regulation target prediction result is highly coordinated with the prior knowledge, and sample clustering result shows superior performance over previous molecular based clustering method.

Conclusions

The results demonstrated the validity and effectiveness of the proposed approach in reconstructing transcriptional networks mediated by TFs through simulated systems and real data.